On Rankin-Cohen Brackets of Hecke Eigenforms and Modular Forms of Half-Integral Weight

YoungJu Choie; Winfried Kohnen; Yichao Zhang

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arXiv · 2405.16745

On Rankin-Cohen Brackets of Hecke Eigenforms and Modular Forms of Half-Integral Weight

YoungJu Choie·Winfried Kohnen·Yichao Zhang

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Abstract

We generalize the linear relation formula between the square of normalized Hecke eigenforms of weight $k$ and normalized Hecke eigenforms of weight $2k$, to Rankin-Cohen brackets of general degree. As an ingredient of the proof, we also generalize a formula of Zagier on the Petersson inner product of Rankin-Cohen brackets involving Eisenstein series.

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YoungJu Choie, Winfried Kohnen, Yichao Zhang. 2024-05-27. On Rankin-Cohen Brackets of Hecke Eigenforms and Modular Forms of Half-Integral Weight. https://arxiv.org/abs/2405.16745

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